Development of the many-body perturbation theory and calculations of atomic properties for optical clocks

The relativistic many-body perturbation theory (MBPT) calculations for matrix elements of divalent atoms and ions is extended to third-order. The one-particle and two-particle contributions are carefully examined and a complete angular reduction of the third-order amplitudes is carried out. Example calculations are performed on beryllium and magnesium isoelectronic sequences. Oscillator strengths, transition probabilities, and lifetimes are calculated for selected ions. Significant improvement in comparison with second-order MBPT results is observed.;The relativistic all-order method is introduced for high-precision calculations of atomic properties in monovalent systems, where all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function are included to all orders of perturbation theory. Energies, reduced electric-dipole matrix elements and lifetimes are calculated and compared with available experiments for the low-lying excited np and nd states in Sr+, Ba+ and Ra+ atoms. Electric-quadrupole moments of the metastable nd3/2 and nd 5/2 states of Ca+, Sr+, and Ba+ are evaluated for the optical clock development applications. Third-order MBPT is used to evaluate the contributions from high partial waves and Breit interaction, and a semi-empirical scaling procedure is carried out to evaluate the remaining omitted correlation corrections. An extensive study of the uncertainties establishes the accuracy of our recommended values as 0.5 - 1% depending on the particular ion. Extra attention is paid to the 5 s-4d5/2 clock transition in 88 Sr+. The scalar polarizabilities of the 5s and 4d5/2 states and the tensor polarizability of the 4d5/2 state are calculated through the summation of individual possible dipole transition contributions. A complete analysis on the uncertainties of the static polarizabilities. The black-body radiation (BBR) shift is evaluated to be 0.250(9) Hz at room temperature, T = 300 K. The dynamic correction to the electric-dipole contribution and the multipolar corrections due to M1 and E2 transitions were estimated and found to be small at the present level of accuracy.;CI + all-order method is used for the calculations of the atomic properties in the divalent systems. This method combines the all-order approach currently used in precision calculations of monovalent system with the configuration-interaction (CI) approach that is applicable for many-electron systems. Energies are calculated in different orders of approximations for several low-lying excited states in the divalent systems from Mg to Hg. The results are compared with experiments. The static and frequency-dependent polarizabilities are evaluated for the lowest nsns 1S0 and nsnp 3P0 states in Sr, Zn, Cd, and Hg atoms. Magic wavelengths are found for the 1 S0 -3 P 0 transitions in those systems by matching the ac Stark shifts of the upper and lower states. The preliminary magic wavelength for the Sr system is in 0.03% agreement with the recent high-precision experiment performed by Brusch et al. [PRL, 96, 103003(2006)]. Other preliminary calculations are performed for the electric-dipole transition matrix elements in Sr, Zn, Cd, and Hg atoms. Transition rates of the ns 2 1S0-nsnp 1P1 resonant line and the ns 2 1S0-nsnp 3P1 intercombination line are evaluated for these systems. Major contributions to the scattering rates are evaluated for the cases where atoms are trapped at their magic wavelengths with a shallow potential depth.